Postpublished at 18:11 British Summer Time 19 June 2015
A nicely constructed point gets Murray's nose in front.
Andy Murray beats Gilles Muller 3-6 7-6 (7-2) 6-4
Briton faces Serbia's Viktor Troicki in last four
Troicki beat John Isner 7-6 (7-5) 6-3
Gilles Simon beats third seed Raonic 4-6 6-3 7-5
Kevin Anderson beats Garcia-Lopez 7-6 7-5
James Gheerbrant
A nicely constructed point gets Murray's nose in front.
John Lloyd
Former British number one on BBC Two
"Murray has been muttering a lot but it hasn't affected him, like it does on some occasions. It's almost frustration but then he seems to get straight back to business."
The apparently nerveless Muller hits the chalk with another thunderbolt, and then cramps Murray up with a clever body-serve. "Shot, mate," Murray congratulates himself sarcastically. But from 40-0, Murray comes charging back - a good return and an unreturnable passing shot get Murray to 40-30. But Muller's serve comes up trumps yet again, and we're going to a tie-break.
John Lloyd
Former British number one on BBC Two
"Muller has a big serve but his groundstrokes have also been awesome and keeping Murray off balance constantly."
The moody mutterings of Murray have begun in earnest by the way - he spent much of the last game berating himself for his lack of movement. But he soothes his teenage angst with another short and sweet service game. Muller will have to serve to stay in it again.
A big test of Muller now, as he serves to stay in the second set. There's a brief flicker of hope for Murray as a vicious return earns him 15-15, but Muller digs out yet another volley and then batters down a big ace to stay on track.
We're at this business end of the second set now - any failure to hold serve here could be fatal. Murray's been down this stretch many times before though, and he keeps his nerve with an emphatic hold.
Muller just hasn't blinked at the net - a vicious top-spin return from Murray that dips wickedly below the tape is coolly dispatched into the corner by the Luxembourger. He got that one up and down, as they say of free-kick takers. Another fine volley by Muller - this time punched on the forehand side - and a big serve draw him level again.
Murray brings the Queen's Club patrons to their feet - OK, prompts a polite ripple of applause - with a magnificent whipped forehand that wrong-foots Muller. A hold to love continues Murray's smooth progress on serve in this second set.
From 40-0, Murray suddenly makes life difficult for the previously assured Muller at the net - a stinging return and a clever slice shot get the Scot to 40-30, but Muller closes out the game with a big serve.
Muller isn't even attempting to chase down the Murray drop-shots any more - as soon as he sees the Scot draw back his racket to unleash a wicked back-spinner, he simply tucks his racket back under his arm with an air of resignation and walks back to receive the next serve. Murray is beginning to find his groove on serve - a big ace keeps him on track on this second set.
I'm not the sure the balding Muller really has quite enough hair to pull off the headband - he's sporting a considerable yardage of cloth for a man with only a few strands on top. Murray gives himself a chance with a lovely return but he can't make the passing shot for 0-30, and Muller compounds his frustration with yet more solid work at the net - just when Murray thinks he's got him with a swooping pass down the line, Muller is there to dead-bat the ball back into the open court.
Piers Newbery
BBC Sport at Queen's
"There is a low hum of astonishment around Centre Court after that clinical set from Muller, whose swinging serve and wicked slice left Murray nowhere to go. The recent return of Jose Mourinho to courtside might inspire a more effective effort from Murray, who has won 32 in a row against left-handers other than Rafael Nadal."
French Open semi-finalist Jo-Wilfried Tsonga has had to pull out of next week's Nottingham ATP World Tour event because of an abdominal strain.
The world number 12 's injury means he will have played no grass-court tennis prior to Wimbledon.
Spain's Feliciano Lopez and British number two James Ward have been confirmed for the Nottingham event, which begins on Monday.
Most parts of the Murray machinery look like they could use a little oiling at the moment, but one bit that is in perfect working order is the drop-shot - Murray nails another one to leave Muller floundering. Some good first serves secure the game.
Muller falters with a volley and Murray paints the line with a terrific passing shot - can that energise him? Muller does his best to dispel the positive vibes with another good volley and a too-hot-to-handle serve. An ace down the T has Murray smashing the ball in frustration, and a wide pass from Murray sees him to the hold.
Murray hasn't been at his best so far - how can he respond to that early setback? The early signs are encouraging - the Scot suddenly finds the ascendancy in those long baseline rallies to earn a solid hold to 15.
John Lloyd
Former British number one on BBC Two
"Credit to Muller. Murray hasn't played great but he hasn't been allowed to. The right thing to think is hold serve, keep the pressure on and at some point Muller's standards will slip. When you play someone who is on a hot streak, you mustn't worry about it because your time will come."
Life is all about the little things. Sleeping in on a rainy day. Feeling the wind in your hair. Or, if you're Andy Murray, having a fruit yoghurt in front of Mock the Week.
"They're lactose free but that's not why I eat them, I just love the taste," says Murray in his latest BBC Sport column, doing a passable impression of a spokesman for a fruit yoghurt company.
He adds: "The new series of Mock the Week is always on around this time of year and I enjoy watching that."
Murray also gives the lowdown on his support team for Wimbledon, including new coach Jonas Bjorkman.
The lob isn't going to win you many points against Muller: at 6'4", the Luxembourger just stretches up a lazy arm like a bear foraging in a fruit tree and bats away the smash. The nerveless Muller gobbles up a midcourt return from Murray, and another big leftie serve completes the job. Super set from Muller, and the shock is on.